HomeworkSolutions_C4 - Problem #1: A differential manometer...

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Problem #1 : A differential manometer is used to measure the pressure difference two points in a pipe of varying cross-sectional area. If the manometric height is h, determine the velocity at point 1 (V1) and 2 (V2). Assume frictionless, steady, constant density flow. Answer: Assumptions: a. Neglect surface tension between the fluid and the mercury (Hg) b. Gradual reduction of the pipe between (1) and (2). Writing the steady flow Bernoulli equation, between (1) and (2) 22 12 11 2 ff pp uh u gg ρρ 2 h + += + + where 2 1 (due to assumption (b)) (1) hh A uu A ⎛⎞ = ⎜⎟ ⎝⎠ and are the cross-sectional areas of the pipe at (1) and (2) respectively A 1 A 2 ( ) Hg f p pg h =− Δ Thus () 1 2 f p p g ρ −= Or 2 2 2 2 1 1 2 Hg f A A ⎡⎤ ⎢⎥ ⎣⎦ Δ Or
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1/2 2 2 2 1 21 1 Hg f A uh A ρ ⎛⎞ ⎡⎤ ⎜⎟ ⎢⎥ ⎝⎠ ⎣⎦ u 1 is thus determined from equation (1). Problem # 2: Starting with the Navier-stokes equation, obtain the velocity profile which describes the incompressible flow between two parallel vertical plates. One plate is at rest, while the other is moving upwards at a constant velocity u s . The distance between the two plates is l . u s l y x Answer: The Navier – Stokes equation in the y–direction is μ u t u u x u u y u u z P y u x u y u z g y x y y y z
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.

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HomeworkSolutions_C4 - Problem #1: A differential manometer...

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